Simple fix; looked up freezer model number, Appliance Parts Pros zeroed in on the key I needed, ordered three as I will probably will need a spare some time in the future :-).
Order was shipped same day, arrived and everything works just fine. Second purchase from this company and everything has been perfect, fast and accurate. Best prices out there too!

Suspected it was the thermostat, since temperature stayed the same at multiple settings over a 24 hr period. There was only three components inside the freezer besides the evaporator, the fan was working, so I decided to just go ahead and replace the thermostat and defrost thermostat. Also replaced the defrost timer by the compressor, just to get all the old parts replaced with new. I had already replaced the compressor, so now I've pretty much have a new freezer. The new parts works great and the freezer now shuts down as it should. Only took me about half an hour to install the parts with just screwdriver.